Frequency dependence of W made simple using a multi-pole approximation

In the GW approximation, the screened interaction W is a non-local and dynamical potential that may have a complex structure in its frequency dependence. A full description of such dependence in a large energy range is in many cases prohibitive: for this reason, it is common practice to approximate it using a plasmon pole (PP) model. The PP approach may however fail for inhomogeneous systems, such as interfaces and defects, and also for some bulk materials, including e.g. metals.
In this work we explore a multi-pole approach for getting an effective representation of W. We show that optimal sampling strategies in the complex plane can lead to accuracies comparable with full-frequency methods at much lower costs, and discuss the application of such strategies to relevant prototype systems.